2.3 Analysis
2.3.3 Properties of the Ensemble
Having discussed the sources individually, we now turn to general conclusions based upon their integrated properties as listed in Table 2.2.
2.3.3.1 Kinematics
All six objects in our sample show well-resolved velocity structure. A visual inspection of Figures 2.2 and 2.3 reveals that four galaxies (Cl 0024+1709, MACS J0451+0006, MACS J0744+3927, and MACS J2135-0102) have smooth velocity gradients suggesting ordered rotation whilst Cl 0949+5153 appears to be a merger with both components showing well-resolved velocity gradients. The dynam- ical state of MACS J0712+5932 is unclear since only the brightest Hα-emitting region is detected with OSIRIS. The nebular emission shows a smooth velocity gradient in MACS J0712+5932, but subtends only four resolution elements in the most highly magnified of the three images and so it is unclear wither the kinematics of MACS J0712+5932 are dominated by rotation, dispersion, or merging.
For the galaxies studied here, the best fit disk models haveχ2ν values which range from 0.4 to 5.9 with a mean of 3.5, indicating agreement typically within 2σfor individual pixels. For reference, disk models for 18 galaxies in the SINS survey which show the most prominent rotation yield best-fitχ2ν values of 0.2–20 to the models of Cresci et al. (2009), so our simple model provides an equally good fit to the lensed galaxies. All galaxies show small-scale deviations from the model as indicated by
the typicalχ2ν >1; these proper motions could be caused by the effects of gravitational instability, or simply be due to the unrelaxed dynamical state indicated by high velocity dispersionsσ > 50 km s−1. We therefore conclude that the model provides an adequate fit to the data and that the velocity fields are consistent with the kinematics of a turbulent rotating disk, except in the case of Cl 0949+5152.
It is illustrative to demonstrate the dramatic improvement in our understanding of the internal dynamics of our sources that arises uniquely through the improved spatial sampling enabled by studying strongly-lensed galaxies. To do this we bin the source-plane data cubes of our targets to a coarser resolution typical of that achievable for unlensed sourcesobserved with an AO-corrected resolution of 0.15′′. We then re-fit the emission lines and extract one-dimensional velocity profiles using the same methods as adopted for the original data. Since the lensing magnification results in µtimes more flux spread overµtimes as many pixels, the binned signal-to-noise ratio is a a factor
√µ higher than equivalent observations of unlensed versions of our galaxies. These simulations therefore represent non-lensed galaxies observed for much longer integrations (∼100 hours!). Even so, the resulting velocity profiles (also shown in Figure 2.3) are considerably inferior to those of our lensed data. A credible rotation curve is only retrieved for Cl 0024+1709, our least magnified galaxy, with important kinematic detail lost in all other objects (for example, MACS J0712+5932 is unresolved). Such poor spatial sampling is insufficient to distinguish between rotation and merging.
More quantitatively, velocity gradients in all of our objects except Cl 0024+1709 are significantly underestimated (typicallyVmax,non−lens/Vmax,lens= 0.6±0.2).
2.3.3.2 Physical Characteristics: Size, Luminosity, and Mass
Next, we examine the integrated physical properties of the lensed galaxies. First we briefly compare the luminosity, size and mass to the general Lyman break population at z≃2–3. In Figure 2.4 we compare the distribution of apparentR-band magnitudes for our sample to that of the Lyman-break population atz∼3 (Shapley et al., 2001). The comparison demonstrates that five of our six galaxies are fainter thanL∗, ranging from 0.1−1.5L∗, with median 0.5L∗well below that of other spatially resolved IFU studies. The intrinsic Hα flux of the arcs is also lower than in other surveys, with a mean and median inferred SFR of 17 M⊙yr−1 (Table 2.2) compared to 26–33 M⊙yr−1 in Law et al. (2009) and F¨orster Schreiber et al. (2009). Comparing the typical spatial extent of the nebular emission to other surveys, the median radius (extent of detected nebular emission) and dynamical mass of the lensed sample are 2.1 kpc and 1.3×1010M⊙, somewhat more extended than the compact galaxies studied by Law et al. (2009) which have median radius of 1.3 kpc and Mdyn= 0.7×1010M⊙. Turning to the dynamics, the flux-weighted mean velocity dispersionsσmeanare perfectly consistent with those studied by Law et al. (2009): both samples span a range of 50–100 km s−1with mean and median 70–75 km s−1, indicating that the two sets of galaxies probe the same range of dynamical
Figure 2.4: Apparent R-band luminosity function of z ∼3 LBGs from Shapley et al. (2001) compared to the distribution of suitably-corrected apparent R magnitudes for our lensed sample as well as the SINS (Forster Schreiber et al. 2009) and Law et al. (2009) samples. We compute the apparent R magnitudes of the IFU samples atz= 3 for an effective wavelengthλ= 600–800 nm depending on the available photometry.
mass density. We note that the median HαFWHM (from longslit spectra; Erb et al. 2006) and stellar mass of ≃6 kpc and 2.9×1010 M⊙ are a better representation of the Law et al. (2009) sample as they do not depend on sensitivity of the data. The SINS survey probes somewhat more extended objects, with median Hα FWHM and stellar mass of ≃8 kpc and M⋆ ≃ 3×1010 M⊙. The mass density and extent of nebular emission of the lensed galaxies are therefore comparable to the more luminous Law et al. (2009) sample and somewhat lower than in the SINS survey. The lensed galaxies are also below the average size and mass for L∗ systems at similar redshifts, with the notable exception of Cl 0024+1709.
Our high resolution data enable us to determine reliable dynamical properties and compare with other IFU observations. In particular we can examine the prevalence of dispersion and rotation as a function of size and dynamical mass. Law et al. (2009) report evidence for dispersion-dominated kinematics in compact low-mass galaxies in contrast to the∼equal mix of rotation, dispersion, and complex/merger kinematics found in the SINS survey (F¨orster Schreiber et al., 2009), although the dispersion-dominated fraction is higher for more compact SINS galaxies. However, this claim is hampered by the small number of resolution elements (≃2–4) subtended by each source (although see Epinat et al. 2009). We can address this issue with the superior resolution offered by gravitational lensing. The relevant relations betweenV /σ and size or dynamical mass is shown in Figure 2.5 for
the five lensed galaxies which are reasonably well fit by disk models compared to the compact LBGs from Law et al. (2009) and the rotation-dominated SINS galaxies described by Cresci et al. (2009), showing that the ratio of velocity shear to dispersion is higher for larger, more massive galaxies.
Furthermore, the general agreement between the lensed sample and other comparison samples is also shown in Figure 2.5 and demonstrates that the dynamics of sub-L∗star-forming galaxies do not differ substantially from more luminous objects.
Noting that many galaxies do not reach an asymptotic velocity within the region probed by our IFU observations, it is likely that larger circular velocities exist in faint outer regions of these galaxies.
Indeed, the spatial extent and mass inferred from longslit spectra and photometry are higher than from relatively shallow IFU data. We therefore also compare the observed velocity gradient and, where appropriate, inclination-corrected rotational velocity as a function of size and dynamical mass in Figure 2.5. The observed velocity gradients of 3/5 lensed galaxies and the entire comparison sample are within 0.3 dex of the median valueVshear/R= 25 km s−1kpc−1. The consistent velocity gradients and correspondingVshear/σobtained with a typicalσ= 75 km s−1(Figure 2.5) suggest that the extended structure in some of the compact objects may in fact host velocity fields comparable to the larger disk galaxies.
While MACS J0451+0006 and MACS J2135-0102 have velocity gradients consistent with the other samples considered here, the clear outlier MACS J0744+3927 demonstrates that at least some small galaxies at this redshift have significant dynamical support from ordered rotation. This galaxy has an inclination-corrected Vc/σ = 1.8+1.2−0.4 at radius R = 1 kpc and a Hα-derived star-formation rate surface density ΣSF R= 0.8±0.3, which is a factor three lower than any galaxy in the dispersion- dominated sample, possibly indicating a later stage of evolution.
Motivated by the relatively large velocity shear and small ΣSF Rof MACS J0744+3927, we explore the possibility that the lowV /σ observed in many compact galaxies is an effect of selecting galaxies in early stages of evolution with large dispersions and star formation rates. This is expected in models of star formation feedback, which predict that mechanical energy introduced by supernovae leads to higher velocity dispersion and hence lowerV /σas ΣSF R increases. In one such model, Dib et al. (2006) simulate the velocity dispersion within the inter-stellar medium of galaxies induced by supernovae energy injection (assuming a 25% feedback efficiency) and predict a correlation between star-formation surface density and velocity dispersion.
To test whether supernova feedback might be responsible for the high dispersion observed in all z>∼2 star-forming galaxies, we show the velocity dispersionσas a function of ΣSF R in Figure 2.6.
For the range of ΣSF Rwith modeled supernova feedback, the observed velocity dispersionsσ= 30–
80 km s−1are much higher than the predictedσ= 10–15 km s−1. We note that the density used in these simulations is ∼30×lower than inferred for the z ≃2 galaxies, so the simulated dispersion is likely overestimated by a factor of∼5. While the data show a slight trend ofσ increasing with
ΣSF R, the observed relation is inconsistent with simulations. We therefore conclude that supernova feedback is insufficient to explain the observed velocity dispersions. Figure 2.6 shows the relation between V /σ–ΣSF R, clearly demonstrating that V /σ decreases with ΣSF R. However, this trend is likely ultimately due to the velocity-size relation: larger galaxies tend to have larger rotation velocities (Figure 2.5) and smaller ΣSF R (Figure 2.6). This is explained by different sensitivities of the data, as deeper spectra (lower ΣSF R) reveal more extended structures at larger radius with larger rotation speed. The velocity-size correlation contributes much more to the observed V /σ–
ΣSF R relation than any correlation between ΣSF R and the velocity dispersion. These data thus do not support the hypothesis thatV /σis strongly affected by the density of star formation: σincreases by less than a factor of 2 over two orders of magnitude in ΣSF R.